Answer:
1: 720
2: [tex]\frac{1}{336}[/tex]
Step-by-step explanation:
1: There are 10 kids in a race so the number of ways such that they come first , second and third=10×9×8
=720
(since the first place is occupied by any one of the ten students i.e. we have ten choices after occupying first position there are only 9 students left for second position and after occupying second for the third position only 8 choices are left)
2: We have to find the probability such that there is no replacement such that we draw 135.
for the first position we have to find the probability([tex]P_{1}[/tex]) that '1' comes out of 8 numbers=[tex]\frac{1}{8}[/tex]
similarly for second choice we could not take 1 as there is no replacement
so probability that 3 comes([tex]P_{2}[/tex]) =[tex]\frac{1}{7}[/tex]
similarly probability that 5 comes at third position([tex]P_{3}[/tex]) = [tex]\frac{1}{6}[/tex]
hence, probability that 135 is drawn= [tex]\frac{1}{8}\times\frac{1}{7}\times\frac{1}{6}=\frac{1}{336}[/tex]
